On the mechanics of thin films and growing surfaces

Mathematics and Mechanics of Solids

Volumn 18, Issue 6, 2013, Pages 561-575

  Holland, Maria A ^a   Kosmata, Tim ^a   Goriely, Alain ^b   Kuhl, Ellen ^c  

^a Stanford University   (United States)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c STANFORD UNIVERSITY   (United States)

Author keywords

Boundary energy; finite elements; plant growth; surface growth; thin films

Indexed keywords

BOUNDARY ENERGIES; COMPUTATIONAL FRAMEWORK; FUNCTIONALIZED SURFACES; OBSTRUCTIVE SLEEP APNOEA; PLANT GROWTH; SPATIAL DISCRETIZATIONS; SURFACE GROWTH; TENSION AND COMPRESSION;

BIOMECHANICS; FINITE ELEMENT METHOD; MEDICAL APPLICATIONS; PLANTS (BOTANY); RIGIDITY; THIN FILMS; TISSUE;

SURFACES;

EID: 84882425830     PISSN: 10812865     EISSN: 17413028     Source Type: Journal    
DOI: 10.1177/1081286513485776     Document Type: Article

References (62)

1. Sachs J Text-book of Botany, Morphological and Physiological. Oxford: Macmillan & Co ; 1875
2. Gager CS Philadelphia, PA: P. Blakiston's Son & Co ; 1916
3. Rausch MK, Kuhl E. On the effect of prestrain and residual stress in thin biological membranes. J Mech Phys Solids.
4. Atkinson GF Lessons in Botany. New York: Henry Hold & Co ; 1900
5. Vandiver R, Goriely A. Tissue tension and axial growth of cylindrical structures in plants and elastic tissues. Euro Phys Lett. 2008 ; 84: 58004
6. Dorfmann A, Haughton DM. Stability and bifurcation of compressed elastic cylindrical tubes. Int J Eng Sci. 2006 ; 44: 1353-1365
7. Thimann KV, Schneider CL. Differential growth in plant tissues. Am J Botany. 1938 ; 25: 627-641
8. Nelson MR, Howard D, Jensen OE, King JR, Rose FRAJ, Waters SL. Growth-induced buckling of an epithelial layer. Biomech Model Mechanobiol. 2011 ; 10: 883-900
9. Vandiver R, Goriely A. Differential growth and residual stress in cylindrical elastic structures. Phil Trans R Soc A. 2009 ; 367: 3607-3630
10. Menzel A. Modelling of anisotropic growth in biological tissues - a new approach and computational aspects. Biomech Model Mechanobiol. 2005 ; 3: 147-171
11. Taber LA, Humphrey JD. Stress-modulated growth, residual stress, and vascular heterogeneity. J Biomech Eng. 2001 ; 123: 528-535
12. Rodriguez EK, Hoger A, McCulloch AD. Stress-dependent finite growth in soft elastic tissues. J Biomech. 1994 ; 27: 455-467
13. Lee EH. Elastic-plastic deformation at finite strains. J Appl Mech. 1969 ; 36: 1-6
14. Ambrosi D, Ateshian GA, Arruda EM, et al. Perspectives on biological growth and remodeling. J Mech Phys Solids. 2011 ; 59: 863-883
15. Garikipati K. The kinematics of biological growth. Appl Mech Rev. 2009 ; 62: 030801
16. Göktepe S, Abilez OJ, Kuhl E. A generic approach towards finite growth with examples of athlete's heart, cardiac dilation, and cardiac wall thickening. J Mech Phys Solids. 2010 ; 58: 1661-1680
17. Menzel A, Kuhl E. Frontiers in growth and remodeling. Mech Res Comm. 2012 ; 42: 1-14
18. Taber LA. Biomechanics of growth, remodeling and morphogenesis. Appl Mech Rev. 1995 ; 48: 487-545
19. Ambrosi D, Mollica F. On the mechanics of a growing tumor. Int J Eng Sci. 2002 ; 40: 1297-1316
20. Himpel G, Kuhl E, Menzel A, Steinmann P. Computational modeling of isotropic multiplicative growth. Comp Mod Eng Sci. 2005 ; 8: 119-134
21. Rausch MK, Dam A, Göktepe S, Abilez OJ, Kuhl E. Computational modeling of growth: systemic and pulmonary hypertension in the heart. Biomech Model Mechanobiol. 2011 ; 10: 799-811
22. Zöllner AM, Abilez OJ, Böl M, Kuhl E. Stretching skeletal muscle: Chronic muscle lengthening through sarcomerogenesis. PLoS ONE. 2012 ; 7 (10). e45661
23. Buganza Tepole A, Ploch CJ, Wong J, Gosain AK, Kuhl E. Growing skin - A computational model for skin expansion in reconstructive surgery. J Mech Phys Solids. 2011 ; 59: 2177-2190
24. Socci L, Rennati G, Gervaso F, Vena P. An axisymmetric computational model of skin expansion and growth. Biomech Model Mechanobiol. 2007 ; 6: 177-188
25. Göktepe S, Abilez OJ, Parker KK, Kuhl E. A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis. J Theor Biol. 2010 ; 265: 433-442
26. McMahon J, Goriely A. Spontaneous cavitation in growing elastic membranes. Math Mech Solids. 2010 ; 15: 57-77
27. Wyczalkowski MA, Chen Z, Filas BA, Varner VD, Taber LA. Computational models for mechanics of morphogenesis. Birth Defects Res C. 2012 ; 96: 132-152
28. Ben Amar M, Goriely A. Growth and instability in elastic tissues. J Mech Phys Solids. 2005 ; 53: 2284-2319
29. Goriely A, BenAmar M. Differential growth and instability in elastic shells. Phys Rev Lett. 2005 ; 94: 198103
30. Zöllner AM, Buganza Tepole A, Kuhl E. On the biomechanics and mechanobiology of growing skin. J Theor Biol. 2012 ; 297: 166-175
31. Kuhl E, Maas R, Himpel G, Menzel A. Computational modeling of arterial wall growth: attempts towards patient-specific simulations based on computer tomography. Biomech Mod Mechanobiol. 2007 ; 6: 321-331
32. Ambrosi D, Guana F. Stress modulated growth. Math Mech Solids. 2007 ; 12: 319-343
33. Dorfmann A, Wilson C, Edgar ES, Peattie RA. Evaluating patient-specific abdominal aortic aneurysm wall stress based on flow-induced loading. Biomech Model Mechanobiol. 2010 ; 9: 127-139
34. Suo Z. Motions of microscopic surfaces in materials. Adv Appl Mech. 1997 ; 33: 193-294
35. Moulton DE, Goriely A. Circumferential buckling instability of a growing cylindrical tube. J Mech Phys Solids. 2011 ; 59: 525-537
36. Steigmann DJ, Ogden RW. Plane deformations of elastic solids with intrinsic boundary elasticity. Proc R Soc Lond A. 1997 ; 453: 853-877
37. Papastavrou A, Steinmann P, Kuhl E. On the mechanics of continua with boundary energies and growing surfaces. J Mech Phys Solids. 2013 ; 61: 1446-1463
38. Laplace PS Traité de Mécanique Céleste. Oeuvres complète. Paris: Gauthier-Villars ; 1805: 771-777.
39. Young T. An essay on the cohesion of fluids. Phil Trans R Soc Lond. 1805 ; 95: 65-87
40. Gurtin ME, Murdoch A. A continuum theory of elastic material surfaces. Arch Rational Mech Anal. 1975 ; 57: 291-323
41. Simha NK, Bhattacharya K. Kinetics of phase boundaries with edges and junctions. J Mech Phys Solids. 1998 ; 46: 2323-2359
42. Gurtin ME, Struthers A. Multiphase thermomechanics with interfacial structure. Arch Rational Mech Anal. 1990 ; 112: 97-160
43. Steigmann DJ, Ogden RW. A necessary condition for energy-minimizing plane deformations of elastic solids with intrinsic boundary elasticity. Math Mech Solids. 1997 ; 2: 3-16
44. Saksono PH, Peric D. On finite element modelling of surface tension. Variational formulation and applications. Part I: Quasistatic problems. Comp Mech. 2006 ; 38: 251-263
45. Javili A, Steinmann P. A finite element framework for continua with boundary energies. Part I: The two-dimensional case. Comp Meth Appl Mech Eng. 2009 ; 198: 2198-2208
46. Steinmann P. On boundary potential energies in deformational and configurational mechanics. J Mech Phys Solids. 2008 ; 56: 772-800
47. Javili A, Steinmann P. A finite element framework for continua with boundary energies. Part II: The three-dimensional case. Comp Meth Appl Mech Eng. 2010 ; 199: 755-765
48. Javili A, Steinmann P. A finite element framework for continua with boundary energies. Part III: The thermomechanical case. Comp Meth Appl Mech Eng. 2011 ; 200: 1963-1977
49. McBride AT, Javili A, Steinmann P, Bargmann S. Geometrically nonlinear continuum theories with surface energies coupled to diffusion. J Mech Phys Solids. 2011 ; 59: 2116-2133
50. Liu SQ, Fung YC. Relationship between hypertension, hypertrophy, and opening angle of zero-stress state of arteries following aortic constriction. J Biomech Eng. 1989 ; 111: 325-335
51. Tsamis A, Cheng A, Nguyen TC, Langer F, Miller DC, Kuhl E. Kinematics of cardiac growth - in vivo characterization of growth tensors and strains. J Mech Behavior Biomed Mat. 2012 ; 8: 165-177
52. Rausch MK, Tibayan FA, Miller DC, Kuhl E. Evidence of adaptive mitral leaflet growth. J Mech Behavior Biomed Mat. 2012 ; 15: 208-217
53. DiCarlo A, Quiligotti S. Growth and balance. Mech Res Comm. 2002 ; 29: 449-456
54. Germain P. La méthode des puissances virtuelles en mécanique des milieux continus. J Mécanique. 1973 ; 12: 135-274
55. Germain P. The method of virtual power in continuum mechanics. Part 2: Microstructure. SIAM J Appl Math. 1973 ; 25: 556-575
56. Zöllner AM, Buganza Tepole A, Gosain AK, Kuhl E. Growing skin - Tissue expansion in pediatric forehead reconstruction. Biomech Mod Mechanobiol. 2012 ; 11: 855-867
57. Goldstein RE, Goriely A. Dynamic buckling of morphoelastic filaments. Phys Rev E. 2006 ; 74: 010901
58. Moulton DE, Goriely A. Possible role of differential growth in airway wall remodeling in asthma. J Appl Physiol. 2011 ; 110: 1003-1012
59. Liao D, Zhao J, Gregersen H. The oesophageal zero-stress state and mucosal folding from a giome perspective. World J Gastroenterol. 2007 ; 13: 1347-1351
60. Kairaitis K. Pharyngeal wall fold influences on the collapsibility of the pharynx. Med Hypotheses. 2012 ; 79: 327-376
61. Xu G, Knutsen AK, Dikranian K, Kroenke CD, Bayly PV, Taber LA. Axons pull on the brain, but tension does not drive cortical folding. J Biomech Eng. 2010 ; 132 (7). 071013
62. Li B, Cao YP, Feng XQ, Gao H. Mechanics of morphological instabilities and surface wrinkling in soft materials: a review. Soft Matter. 2012 ; 8: 5728-5745